With the values of \(z\)  being limited up to half of the spatial extent of the lattice, the reconstruction of the \(x\) -dependence is an ill-posed inverse problem that does not have a unique solution. To avoid imposing assumptions like \(F_X\)  being zero beyond some \(z_{\rm max}\) , we use the model-independent Backus-Gilbert reconstruction method. More details on the implementation can be found in [1]}, [2]}. The last step of the calculation is to match the quasi-GPDs, \(G_{X,{\rm Q}}\) , to the light-cone GPDs, \(G_X\) , via a kernel calculated in perturbation theory,
\(G_{X,{\rm Q}}(x,\xi ,t,P_3,\mu ) = \int _{-1}^1 \frac{dy}{|y|} C_X\left(\frac{x}{y},\frac{\xi }{y},\frac{\mu }{yP_3},r\right) G_X(y,\xi ,t,\mu ) + \mathcal {O}\left(\frac{m^2}{P_3^2}, \frac{t}{P_3^2}, \frac{\Lambda _QCD^2}{x^2P_{3_{\phantom{L}}}^2}\right)\,.\) 
